Geometrically nonlinear nonlocal strain gradient vibration of FG shear deformable curved nanobeams

This article focuses on studying the nonlinear vibration of functionally graded (FG) curved nanobeams resting on the Pasternak-Winkler elastic foundation based on the nonlocal strain gradient theory along with the first-order shear deformation beam theory (FSDBT) considering von-Karman hypothesis. The Hamilton principle is applied to extract three nonlinear motion equations and the Galerkin method (GM) is utilized to spatially reduce the differential equations. The analytical approach based on the two-step perturbation method (TSPM) was employed to deal with nonlinear governing equations. To verify the outcomes of the present article, the natural frequencies and frequency ratios are validated with those reported in the literature. Subsequently, the results presented in this paper are of a significant point to describe the nonlinear vibration of FG curved nanobeams in conjunction with different parameters.